Probably not any that you will notice. Just make sure you put passwords on everything so the neighbors can't "steal" your bandwidth. Personally, I use hardwire. Most computers come with on-board NIC cards and if they don't you can buy one for $10 at Wal-Mart. Cable is about $0.29 at Radio Shack and you can buy pre-cut cable with ends for just a bit more. A friend of mine has wireless and has had a few problems with uninvited guests and connectivity issues. These come and go. As far as how to run the wire, you will have to use your imagination. I run ours under the wall molding by the floor. It's temporary and tasteful. Holes in sheetrock can be patched very easily if need be. From the drawing, it looks like you can go right through the closet wall.

It's totally up to you. I use hard wire and have NEVER had a problem. It's tried and true, but you have to run wires where wireless can be affected by so many variables, but it's more convenient.

Good luck.